Extracting extremal features from 3D volume data

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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Extremal features are implicit curve, surface and points features defined on 3D data with a scalar field and a tensor field. The extremal curves, surfaces and points are the set of points reaches directional extremal, under different direction vector fields (generated from the tensor field). Given a scalar field and a tensor field, We extract 3 extremal features from 3D volume data using different algorithms based on a uniform spacial grid. To extract extremal curves, we developed a parallel vectors extracting method. Parallel vectors (PV), the loci where two given vector fields are parallel, are commonly used to generate line-type features in 3D for data visualization. We propose the first provably correct test that determines the parity of the number of PV points on a cell face. The test can guide PV-extraction algorithms to ensure closed curves wherever the input fields are continuous, which we exemplify in extracting ridges and valleys (extremal curves) of scalar functions. We also implement the existing extremal surface extracting algorithm to extract ridge and valley surfaces (extremal surfaces). Similar to the parity test of extremal curves, we develop a parity test of number of extremal points containing in a cell. For any input 3D volume data, we can extract all 3 extremal features based on same scalar and tensor field generated from the data, and display them in user defined ways.